Notice that the assignments are made to the terms location(x) and
color(x) rather than to simple variables as in (16).
In order to avoid
contradiction as well as to describe moving and painting, we need axioms
that these objects are different. We have axioms

Using situations as frames in this way makes certain commitments that
might not be immediately obvious. Consider distance(x1,x2) which is
supposed to be some function of location(x1) and location(x2).

We will not want to use c(distance(x1,x2),s), because our axioms
would not permit c(distance(x1,x2),s) to change when the locations
changed. Instead we use another function value(term,s) and the
equations

The effect is to take location(x) and color(x) as primary
fluents and distance(x,y) as a secondary fluent whose
value is dependent on the values of primary fluents. Deciding what
fluents to make primary is an epistemological decision, i.e. it is a
feature of the theory being used. clear(x) must also be a
secondary fluent.